Rangeintersection

Rangeintersection is a concept found in various fields, particularly in mathematics, computer science, and statistics, that refers to the set of values that are common to two or more given ranges. A range is typically defined by a lower and an upper bound. For example, the range [2, 5] includes all numbers between 2 and 5, inclusive. The intersection of two ranges, [2, 5] and [4, 7], would be [4, 5], as these are the numbers present in both ranges.

The calculation of a range intersection involves comparing the bounds of the ranges. For two ranges, [a, b] and [c, d], the intersection is given by [max(a, c), min(b, d)]. If the calculated lower bound is greater than the calculated upper bound, then the intersection is empty, meaning there are no common values between the original ranges. This concept is crucial in algorithms that deal with scheduling, resource allocation, and data filtering. For instance, in scheduling, range intersection can determine available time slots that overlap between two individuals' calendars. In computer graphics, it's used to determine visible portions of objects. The principle extends to multi-dimensional ranges as well, where the intersection is the region containing points common to all specified multi-dimensional ranges.